Lee D. Peterson

Estimation of reciprocal residual flexibility from experimental modal data

A technique is presented for estimating the residual flexibility between nonexcited structural degrees of freedom from experimental structural vibration data. Using this method, one can include the residual flexibility estimated from modal measurements in the computation of measured flexibility for experiments with incomplete reciprocity, i.e., when the response and excitation measurement sensors are not fully collocated. The method can also be used to estimate the unknown entries in the residual flexibility matrix for experimental component mode synthesis when excitations are not provided at all interface degrees of freedom. A general solution is presented that contains an unknown positive semidefinite contribution. The general solution satisfies modal orthogonality in the limit that all of the structural degrees of freedom are instrumented and when the positive semidefinite contribution lies in a nullspace defined by the stiffness matrix and the modal flexibility. With a limited number of measurements, modal orthogonality is shown to be satisfied to the extent that the measured modes are preserved by static condensation. A rank-deficient solution is presented that allows the residual to be used in the computation of the flexibility matrix without further modeling assumptions. Numerical and experimental results that demonstrate the application of the method to both flexibility matrix convergence and experimental component mode synthesis are presented.

Rationale for Defining Structural Requirements for Large Space Telescopes

The present paper presents a rationale for defining structural requirements for future large space telescope systems. The rationale is based on bounding analyses for the deformation of telescope mirrors in response to expected on-orbit disturbance loads and consideration of active control systems that partially compensate for these deformations. It is shown that the vibration frequency of the telescope structure, independent of telescope size, determines the passive structural stability and requirements for an active control system. This means that future large telescopes with low vibration frequencies will necessarily allocate increased active control error budget in proportion to the square of the vibration frequency. Parametric analyses are also presented for the vibration response of two representative mirror architectures: a tensioned membrane mirror and a truss-supporte d segmented mirror. These examples demonstrate that meeting a specified frequency requirement will require a trade between structural mass fraction and depth of the primary mirror support structure regardless of the structural architecture.

Dimensional Repeatability of an Elastically Folded Composite Hinge for Deployed Spacecraft Optics

A new type of folded composite hinge is investigated for its use in precision deployable spacecraft structures. The hinge is an integral feature of a composite tube intended for use as a structural truss member. The design of the hinge allows the tube to be elastically folded for stowage even with tube wall thicknesses from 0.4 to 1.7 mm. Whether the large but primarily elastic folding stresses impart permanent deformations to the tube after it is deployed is experimentally assessed. The data show that any such permanent strain induces tip deformations, identified as microscopic plastic behavior, of no more than 2.5 μ axially and 9 p laterally, depending on the composite layup. This deployment repeatability is comparable to prior measurements of mechanical deployables. Moreover, stow duration and number of stows have no measurable effect, once the initial stow-deploy cycle has been completed. There is always a significant viscoelastic creep recovery following deployment that increases with stowage time. However, this viscoelastic creep is recovered. An exponential curve fit of the creep time response shows that the time constants of the viscoelastic recovery are independent of stow duration.

Submicron Mechanical Stability of a Prototype Deployable Space Telescope Support Structure

This paper describes the experimental characterization of the microdynamics of a prototype deployable telescope support structure. The experimental methods described separate thermal from mechanical microdynamics to within 0.003°C. It is shown that the intentional application of impulses to the structure, following the initial deployment, apparently stabilizes the microdynamics to within approximately 250 nanometers. This level is comparable to the background vibration of the test article. A model is presented that correlates well with the data, suggesting that this effect is due to the dynamically induced relaxation of strain energy stored by friction mechanisms within the structure.

A Revolute Joint With Linear Load-Displacement Response for Precision Deployable Structures

A Revolute Joint With Linear Load-Displacement Response for PrecisionDeployable StructuresMark S. LakeNASA Langley Research CenterHampton, VAAndPeter A. Warren and Lee D. PetersonUniversity of ColoradoBoulder, COPresented at the 37th AIAA / ASME/ASCE/AHS / ASCStructures, Structural Dynamics, and Materials Conference

Research on the problem of high-precision deployment for large-aperture space-based science instruments

The present paper summarizes results from an ongoing research program conducted jointly by the University of Colorado and NASA Langley Research Center since 1994. This program has resulted in general guidelines for the design of high-precision deployment mechanisms, and tests of prototype deployable structures incorporating these mechanisms have shown microdynamically stable behavior (i.e., dimensional stability to parts per million). These advancements have resulted from the identification of numerous heretofore unknown microdynamic and micromechanical response phenomena, and the development of new test techniques and instrumentation systems to interrogate these phenomena. In addition, recent tests have begun to interrogate nanomechanical response of materials and joints and have been used to develop an understanding of nonlinear nanodynamic behavior in microdynamically stable structures. The ultimate goal of these efforts is to enable nano-precision active control of micro-precision deployable structures (i.e., active control to a resolution of parts per billion).

Method for structural model update using dynamically measured static flexibility matrices

A new method is presented for parametric correction of full-order analytical stiffness matrices from reduced-order dynamically measured static flexibility matrices. The measured static flexibility matrix is formed using modal data in conjunction with a residual flexibility estimate. The algorithm corrects model parameters by minimizing a static flexibility matrix error residual constructed for measurement degrees of freedom only. By utilizing a flexibility matrix residual instead of one derived using stiffness matrices, numerical problems associated with inverting a rank-deficient measured flexibility matrix are avoided. Posing the problem in terms of flexibility matrices also avoids the problems of modal correspondence, mode selection, and modal truncation. In addition, incorporating static reduction relationships into the error residual makes prior eigenvector expansion or model reduction unnecessary. Two formulations for the error residual are presented: an explicit inverse formulation and one derived from a pseudoinverse relationship. The second leads to an exact linear update problem when all of the model degrees of freedom are measured. Numerical simulation results demonstrate that both formulations are capable of localizing and quantifying local stiffness errors in a full-order finite element model from reduced-order measurements. Experimental results for a cantilever beam structure are also presented.

Implications of structural design requirements for selection of future space telescope architectures

Decisions about structural architecture for future large space observatories will influence how overall optical stability scales with observatory size. This is examined using basic structural design analyses that relate overall stability requirements to telescope structural modal frequency and damping ratio. In this way, the influence of certain system level architectural choices on the performance can be assessed. In particular, trades between structural depth and optical correction requirements is examined, and compared against other design parameters such as the material specific modulus. For representative configurations and loads, the required optical correction increases with dimension to the fourth power, but reduces with the square of the structural depth and in proportion to the material specific modulus; areal density has no direct affect. This means that, unless the structural architecture improves with dimension, the optical error produced in a 6-meter telescope might increase by a factor of 123:1 for a 20-meter telescope and 77000:1 for a 100-meter telescope. If the structural depth, however, increases in proportion to telescope dimension, these requirements can be reduced by two orders of magnitude. Architectural options for achieving these benefits are discussed, with particular emphasis on considerations of the deployment or assembly scheme.

Geometric Imperfection Effects in an Elastically Deployable Isogrid Column

The experimental study and analysis of a novel gossamer structural component is described. The component is a 3-m-long thin-walled isogrid column prototype that may be elastically stowed and deployed. The column has a diameter of 0.318 m, with a linear density of 46 g/m. The static and dynamic mechanical responses of the deployed prototype are examined and compared to an idealized model. These comparisons indicate global stiffness ranging from11to28%andbucklingstrengthsfrom7to37%ofthetheoreticallyidealperformance.Initiallocalcurvatures approaching the thickness of the isogrid ribs are found to be the primary source of this performance reduction. A modeling approach based on the postbuckled response of individual isogrid ribs is proposed for predicting the global effects of local imperfections, and good agreement with the test results is found. In general, initial rib curvatures greater than 10% of the rib thickness are predicted to result in signie cant degradations of the global structural performance.

Predictive Elastothermodynamic Damping in Finite Element Models by Using a Perturbation Formulation

A method is presented by which elastothermodynamic damping can be included in finite element formulations for design analysis. In this method, elastothermodynamic damping theory is combined with a perturbation method previously developed for viscoelastic modeling. A key aspect of this approach is that it projects elastothermodynamic damping onto the undamped mode shapes of the structure. A finite element formulation is developed and presented for beams in both bending and extension. The finite element formulation creates nonsparse, nonsymmetric damping and stiffness matrices. Results with this method for various cases are discussed. After validation against the classic Zener model damping prediction, the method is applied to the analysis of damping in a three-dimensional truss. The results show that elastothermodynamic damping is higher for modes with a larger portion of their strain energy due to local member bending rather than extension. Through examples it is shown that to maximize elastothermodynamic damping in a truss, both the member cross section and the truss mode shapes must be considered.